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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="intrusive.sg_set_multiset"></a><a class="link" href="sg_set_multiset.html" title="Intrusive scapegoat tree based associative containers: sg_set, sg_multiset and sgtree">Intrusive scapegoat tree based
    associative containers: sg_set, sg_multiset and sgtree</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_containers">sg_set,
      sg_multiset and sgtree containers</a></span></dt>
<dt><span class="section"><a href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_example">Example</a></span></dt>
</dl></div>
<p>
      A scapegoat tree is a self-balancing binary search tree, that provides worst-case
      O(log n) lookup time, and O(log n) amortized insertion and deletion time. Unlike
      other self-balancing binary search trees that provide worst case O(log n) lookup
      time, scapegoat trees have no additional per-node overhead compared to a regular
      binary search tree.
    </p>
<p>
      A binary search tree is said to be weight balanced if half the nodes are on
      the left of the root, and half on the right. An a-height-balanced tree is defined
      with defined with the following equation:
    </p>
<p>
      <span class="bold"><strong><span class="emphasis"><em>height(tree) &lt;= log1/a(tree.size())</em></span></strong></span>
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          <span class="bold"><strong><span class="emphasis"><em>a == 1</em></span></strong></span>: A tree forming
          a linked list is considered balanced.
        </li>
<li class="listitem">
          <span class="bold"><strong><span class="emphasis"><em>a == 0.5</em></span></strong></span>: Only a
          perfectly balanced binary is considered balanced.
        </li>
</ul></div>
<p>
      Scapegoat trees are loosely <span class="emphasis"><em>a-height-balanced</em></span> so:
    </p>
<p>
      <span class="bold"><strong><span class="emphasis"><em>height(tree) &lt;= log1/a(tree.size()) + 1</em></span></strong></span>
    </p>
<p>
      Scapegoat trees support any a between 0.5 and 1. If a is higher, the tree is
      rebalanced less often, obtaining quicker insertions but slower searches. Lower
      a values improve search times. Scapegoat-trees implemented in <span class="bold"><strong>Boost.Intrusive</strong></span>
      offer the possibility of <span class="bold"><strong>changing a at run-time</strong></span>
      taking advantage of the flexibility of scapegoat trees. For more information
      on scapegoat trees see <a href="http://en.wikipedia.org/wiki/Scapegoat_tree" target="_top">Wikipedia
      entry</a>.
    </p>
<p>
      Scapegoat trees also have downsides:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          They need additional storage of data on the root (the size of the tree,
          for example) to achieve logarithmic complexity operations so it's not possible
          to offer <code class="computeroutput"><span class="identifier">auto_unlink</span></code> hooks.
          The size of an empty scapegoat tree is also considerably increased.
        </li>
<li class="listitem">
          The operations needed to determine if the tree is unbalanced require floating-point
          operations like <span class="emphasis"><em>log1/a</em></span>. If the system has no floating
          point operations (like some embedded systems), scapegoat tree operations
          might become slow.
        </li>
</ul></div>
<p>
      <span class="bold"><strong>Boost.Intrusive</strong></span> offers 3 containers based
      on scapegoat trees: <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__set.html" title="Class template sg_set">sg_set</a></code>,
      <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__multiset.html" title="Class template sg_multiset">sg_multiset</a></code> and
      <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sgtree.html" title="Class template sgtree">sgtree</a></code>. The first two
      are similar to <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1set.html" title="Class template set">set</a></code> or <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1multiset.html" title="Class template multiset">multiset</a></code> and the latter is a generalization
      that offers functions both to insert unique and multiple keys.
    </p>
<p>
      The memory overhead of these containers with Boost.Intrusive hooks is 3 pointers.
    </p>
<p>
      An empty, <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__set.html" title="Class template sg_set">sg_set</a></code>, <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__multiset.html" title="Class template sg_multiset">sg_multiset</a></code> or <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sgtree.html" title="Class template sgtree">sgtree</a></code>
      has also the size of 3 pointers, two integers and two floating point values
      (equivalent to the size of 7 pointers on most systems).
    </p>
<p>
      <span class="bold"><strong>Boost.Intrusive</strong></span> scapegoat associative containers
      don't use their own hook types but plain Binary search tree hooks. See <a class="link" href="bst_hooks.html" title="Binary search tree hooks: bs_set_base_hook and bs_set_member_hook">Binary search tree hooks: bs_set_base_hook and
      bs_set_member_hook</a> section for more information about these hooks.
    </p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.sg_set_multiset.sg_set_multiset_containers"></a><a class="link" href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_containers" title="sg_set, sg_multiset and sgtree containers">sg_set,
      sg_multiset and sgtree containers</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">sg_set</span><span class="special">;</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">sg_multiset</span><span class="special">;</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="special">...</span><span class="identifier">Options</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">sgtree</span><span class="special">;</span>
</pre>
<p>
        These containers receive the same options explained in the section <a class="link" href="usage.html" title="How to use Boost.Intrusive">How to use Boost.Intrusive</a>:
      </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
            <span class="bold"><strong><code class="computeroutput"><span class="identifier">base_hook</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Hook</span><span class="special">&gt;</span></code></strong></span>
            / <span class="bold"><strong><code class="computeroutput"><span class="identifier">member_hook</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Hook</span><span class="special">,</span> <span class="identifier">Hook</span> <span class="identifier">T</span><span class="special">::*</span> <span class="identifier">PtrToMember</span><span class="special">&gt;</span></code></strong></span>
            / <span class="bold"><strong><code class="computeroutput"><span class="identifier">value_traits</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">ValueTraits</span><span class="special">&gt;</span></code></strong></span>:
            To specify the hook type or value traits used to configure the container.
            (To learn about value traits go to the section <a class="link" href="value_traits.html" title="Containers with custom ValueTraits">Containers
            with custom ValueTraits</a>.)
          </li>
<li class="listitem">
            <span class="bold"><strong><code class="computeroutput"><span class="identifier">size_type</span><span class="special">&lt;</span><span class="keyword">typename</span>
            <span class="identifier">SizeType</span><span class="special">&gt;</span></code></strong></span>:
            To specify the type that will be used to store the size of the container.
            Default: <code class="computeroutput"><span class="identifier">size_type</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span><span class="special">&gt;</span></code>
          </li>
</ul></div>
<p>
        And they also can receive additional options:
      </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
            <span class="bold"><strong><code class="computeroutput"><span class="identifier">compare</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Compare</span><span class="special">&gt;</span></code></strong></span>:
            Comparison function for the objects to be inserted in containers. The
            comparison functor must induce a strict weak ordering. Default: <code class="computeroutput"><span class="identifier">compare</span><span class="special">&lt;</span>
            <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">&lt;</span><span class="identifier">key_type</span><span class="special">&gt;</span>
            <span class="special">&gt;</span></code>
          </li>
<li class="listitem">
            <span class="bold"><strong><code class="computeroutput"><span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">Enable</span><span class="special">&gt;</span></code></strong></span>:
            When this option is deactivated, the scapegoat tree loses the ability
            to change the balance factor a at run-time, but the size of an empty
            container is reduced and no floating point operations are performed,
            normally increasing container performance. The fixed a factor that is
            used when this option is activated is <span class="emphasis"><em>1/sqrt(2) ~ 0,70711</em></span>.
            Default: <code class="computeroutput"><span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
          </li>
<li class="listitem">
            <span class="bold"><strong><code class="computeroutput"><span class="identifier">key_of_value</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">KeyOfValueFunctionObject</span><span class="special">&gt;</span></code></strong></span>:
            A function object that will define the <code class="computeroutput"><span class="identifier">key_type</span></code>
            of the value type to be stored. This type will allow a map-like interface.
            See <a class="link" href="map_multimap.html" title="Map and multimap-like interface for associative containers">Map and multimap-like interface
            with set and multiset</a> for details. Default: <code class="computeroutput"><span class="identifier">key_type</span></code>
            is equal to <code class="computeroutput"><span class="identifier">value_type</span></code>
            (set-like interface).
          </li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="intrusive.sg_set_multiset.sg_set_multiset_example"></a><a class="link" href="sg_set_multiset.html#intrusive.sg_set_multiset.sg_set_multiset_example" title="Example">Example</a>
</h3></div></div></div>
<p>
        Now let's see a small example using binary search tree hooks and <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__set.html" title="Class template sg_set">sg_set</a></code>/ <code class="computeroutput"><a class="link" href="../doxygen/classboost_1_1intrusive_1_1sg__multiset.html" title="Class template sg_multiset">sg_multiset</a></code>
        containers:
      </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">intrusive</span><span class="special">/</span><span class="identifier">sg_set</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">vector</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">functional</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cassert</span><span class="special">&gt;</span>

<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intrusive</span><span class="special">;</span>

<span class="keyword">class</span> <span class="identifier">MyClass</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">bs_set_base_hook</span><span class="special">&lt;&gt;</span>
<span class="special">{</span>
   <span class="keyword">int</span> <span class="identifier">int_</span><span class="special">;</span>

   <span class="keyword">public</span><span class="special">:</span>
   <span class="comment">//This is a member hook</span>
   <span class="identifier">bs_set_member_hook</span><span class="special">&lt;&gt;</span> <span class="identifier">member_hook_</span><span class="special">;</span>

   <span class="identifier">MyClass</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span>
      <span class="special">:</span>  <span class="identifier">int_</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span>
      <span class="special">{}</span>
   <span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">)</span>
      <span class="special">{</span>  <span class="keyword">return</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">int_</span> <span class="special">&lt;</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span>  <span class="special">}</span>
   <span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">&gt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">)</span>
      <span class="special">{</span>  <span class="keyword">return</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">int_</span> <span class="special">&gt;</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span>  <span class="special">}</span>
   <span class="keyword">friend</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MyClass</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">)</span>
      <span class="special">{</span>  <span class="keyword">return</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">int_</span> <span class="special">==</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">int_</span><span class="special">;</span>  <span class="special">}</span>
<span class="special">};</span>

<span class="comment">//Define an sg_set using the base hook that will store values in reverse order</span>
<span class="comment">//and won't execute floating point operations.</span>
<span class="keyword">typedef</span> <span class="identifier">sg_set</span>
   <span class="special">&lt;</span> <span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">compare</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">greater</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">floating_point</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">BaseSet</span><span class="special">;</span>

<span class="comment">//Define an multiset using the member hook</span>
<span class="keyword">typedef</span> <span class="identifier">member_hook</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">bs_set_member_hook</span><span class="special">&lt;&gt;,</span> <span class="special">&amp;</span><span class="identifier">MyClass</span><span class="special">::</span><span class="identifier">member_hook_</span><span class="special">&gt;</span> <span class="identifier">MemberOption</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">sg_multiset</span><span class="special">&lt;</span> <span class="identifier">MyClass</span><span class="special">,</span> <span class="identifier">MemberOption</span><span class="special">&gt;</span>   <span class="identifier">MemberMultiset</span><span class="special">;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;::</span><span class="identifier">iterator</span> <span class="identifier">VectIt</span><span class="special">;</span>

   <span class="comment">//Create several MyClass objects, each one with a different value</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">MyClass</span><span class="special">&gt;</span> <span class="identifier">values</span><span class="special">;</span>
   <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">100</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>  <span class="identifier">values</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">MyClass</span><span class="special">(</span><span class="identifier">i</span><span class="special">));</span>

   <span class="identifier">BaseSet</span> <span class="identifier">baseset</span><span class="special">;</span>
   <span class="identifier">MemberMultiset</span> <span class="identifier">membermultiset</span><span class="special">;</span>

   <span class="comment">//Now insert them in the reverse order in the base hook sg_set</span>
   <span class="keyword">for</span><span class="special">(</span><span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">){</span>
      <span class="identifier">baseset</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
      <span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(*</span><span class="identifier">it</span><span class="special">);</span>
   <span class="special">}</span>

   <span class="comment">//Change balance factor</span>
   <span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">balance_factor</span><span class="special">(</span><span class="number">0.9f</span><span class="special">);</span>

   <span class="comment">//Now test sg_sets</span>
   <span class="special">{</span>
      <span class="identifier">BaseSet</span><span class="special">::</span><span class="identifier">reverse_iterator</span> <span class="identifier">rbit</span><span class="special">(</span><span class="identifier">baseset</span><span class="special">.</span><span class="identifier">rbegin</span><span class="special">());</span>
      <span class="identifier">MemberMultiset</span><span class="special">::</span><span class="identifier">iterator</span> <span class="identifier">mit</span><span class="special">(</span><span class="identifier">membermultiset</span><span class="special">.</span><span class="identifier">begin</span><span class="special">());</span>
      <span class="identifier">VectIt</span> <span class="identifier">it</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()),</span> <span class="identifier">itend</span><span class="special">(</span><span class="identifier">values</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span>

      <span class="comment">//Test the objects inserted in the base hook sg_set</span>
      <span class="keyword">for</span><span class="special">(;</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">,</span> <span class="special">++</span><span class="identifier">rbit</span><span class="special">)</span>
         <span class="keyword">if</span><span class="special">(&amp;*</span><span class="identifier">rbit</span> <span class="special">!=</span> <span class="special">&amp;*</span><span class="identifier">it</span><span class="special">)</span>   <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>

      <span class="comment">//Test the objects inserted in the member hook sg_set</span>
      <span class="keyword">for</span><span class="special">(</span><span class="identifier">it</span> <span class="special">=</span> <span class="identifier">values</span><span class="special">.</span><span class="identifier">begin</span><span class="special">();</span> <span class="identifier">it</span> <span class="special">!=</span> <span class="identifier">itend</span><span class="special">;</span> <span class="special">++</span><span class="identifier">it</span><span class="special">,</span> <span class="special">++</span><span class="identifier">mit</span><span class="special">)</span>
         <span class="keyword">if</span><span class="special">(&amp;*</span><span class="identifier">mit</span> <span class="special">!=</span> <span class="special">&amp;*</span><span class="identifier">it</span><span class="special">)</span> <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
   <span class="special">}</span>
   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
</div>
</div>
<div class="copyright-footer">Copyright © 2005 Olaf Krzikalla<br>Copyright © 2006-2015 Ion Gaztanaga<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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